Geometrical Optics Problems

7/28/2019 Geometrical Optics Problems

1/19

Index

1. Key Concepts2. Exercise I

3. Exercise II

4. Exercise III

5. Exercise IV

6. Answer Key

7. 34 Yrs. Que. from IIT-JEE

8. 10 Yrs. Que. from AIEEE

Subject : PHYSICS

Topic : GEOMETRICAL OPTICS

Students Name :______________________

Class :______________________

Roll No. :______________________

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Page2of20GEOMETRICALOPTICS

KEY CONCEPTS

1. LAWS OF REFLECTION :

(i) The incident ray (AB), the reflected ray (BC) and normal (NN') to the surface (SC') of reflection at the

point o f incidence (B) lie in the same plane. This plane is called the plane of incidence (also plane of

reflection).

(ii) The angle of incidence (the angle between normal and the incident

ray) and the angle of reflection (the angle between the reflected rayand the normal) are equal

i = r

2. OBJECT :

(a) Real : Point from which rays actually diverge.

(b) Virtual : Point towards which rays appear to converge

3. IMAGE :

Image is decided by reflected or refracted rays only. The point image for a mirror is that point

(i) Towards which the rays reflected from the mirror, actually converge (real image).

OR

(ii) From which the reflected rays appear to diverge (virtual image) .

4. CHARACTERISTICS OF REFLECTION BY A PLANE MIRROR :

(a) The size of the image is the same as that of the object.

(b) For a real object the image is virtual and for a virtual object the image is real.

(c) For a fixed incident light ray, if the mirror be rotated through an angle the reflected ray turns through

an angle 2.

5. SPHERICAL MIRRORS :

Concave Convex

6. PARAXIAL RAYS : Rays which forms very small angle with axis are called paraxial rays.

7. SIGN CONVENTION:

We follow cartesian co-ordinate system convention according to which

(a) The pole of the mirror is the origin .

(b) The direction of the incident rays is considered as positive x-axis.

(c) Vertically up is positive y-axis.

Note : According to above convention radius of curvature and focus of concave mirror is negative and ofconvex mirror is positive.

8. MIRROR FORMULA :1

f=

1 1

v u+ .

f = x- coordinate of focus ; u = x-coordinate of object ;

v = x-coordinate of image

Note : Valid only for paraxial rays.


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9. TRANSVERSE MAGNIFICATION : m =h

h2

1

= v

u

h2

= y co-ordinate of images h1= y co-ordinate of the object

(both perpendicular to the principle axis of mirror)

10. NEWTON'S FORMULA :

Applicable to a pair of real object and real image position only . They are called conjugate positions

or foci. X,Y are the distance along the principal axis of the real object and real image respectively fromthe principal focus .

XY = f2

11. OPTICAL POWER : Optical power of a mirror (in Diopters) = 1

f;

f = focal length (in meters) with sign .

REFRACTION -PLANE SURFACE

1. LAWS OF REFRACTION (AT ANY REFRACTING SURFACE) :

(i) The incident ray (AB), the normal (NN') to the refracting surface (II') at the point of incidence (B) and

the refracted ray (BC) all lie in the same plane called the plane of incidence or plane of refraction .

(ii)Sin i

Sin r= Constant :

for any two given media and for light of a given wave length. This is known as

SNELL'S Law .

Sin i

Sin r=

1n

2=

n

n2

1

=v

v1

2

=

1

2

Note : Frequency of light does not change during refraction .

2. DEVIATION OF A RAY DUE TO REFRACTION :

3. REFRACTION THROUGH A PARALLEL SLAB :

(i) Emerged ray is parallel to the incident ray, if medium is same onboth sides.

(ii) Lateral shift x =t i r

r

sin( )

cos

t = thickness of slab

Note : Emerged ray will not be parallel to the incident ray if the medium on both the sides

are different .


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4. APPARENT DEPTH OF SUBMERGED OBJECT :

(h < h)

at near normal incidence h =

2

1

h

Note : h and h' are always measured from surface.

5. CRITICAL ANGLE & TOTAL INTERNAL REFLECTION ( T. I. R.)

CONDITIONS OF T. I. R.(i) Ray going from denser to rarer medium

(ii) Angle of incidence should be greater than the critical angle (i > c) .

Critical angle C = sin-1

i

r

n

n

6. REFRACTION THROUGH PRISM :

1. = (i + i) - (r + r)2. r + r = A3. Variation ofversus i (shown in diagram) .4. There is one and only one angle of incidence for which the angle

of deviation is minimum.

When = m then i = i & r = r , the ray passes symetricallyabout the prism, & then

n =[ ]

[ ]

sin

sin

A m

A

+

2

2

, where n = absolute R.I. of glass .

Note : When the prism is dipped in a medium thenn = R.I. of glass w.r.t. medium .


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5. For a thin prism ( A10o) ; = ( n 1 ) A6. DISPERSION OF LIGHT :

The angular spilitting of a ray of white light into a number of components when it is refracted in a medium

other than air is called Dispersion of Light.7. Angle of Dispersion : Angle between the rays of the extreme colours in the refracted (dispersed) light

is calledAngle of Dispersion . = v

r

.

8. Dispersive power () of the medium of the material of prism .

= angular dispersiondeviation of mean ray yel low( )

For small angled prism ( A10o)

=

v R

y

=

n n

nv R

1 ; n =

n nv R+

2

nv, n

R& n are R. I. of material for violet, red & yellow colours respectively .

9. COMBINATION OF TWO PRISMS :

(i) ACHROMATIC COMBINATION : It is used for deviation without dispersion .

Condition for this (nv

-nr) A = (n

v- n

r) A .

Net mean deviation =

n nv R+

21 A

+

n nv R

2 1A .

or + = 0 where, are dispersive powers for the two prisms & , are the mean deviation.

(ii) DIRECT VISION COMBINATION: It is used for producing disperion without deviation condition

for thisn nv R+

21 A =

+

n nv R

21 A .

Net angle of dispersion = (nv- n

r) A = (n

v - n

r) A .

REFRACTION AT SPERICAL SURFACE

1.(a)Ruv

1212 =

v, u & R are to be kept with signas v = PI

u = PO

R = PC

(Note radius is with sign)

(b) m = u

v

2

1

2. LENS FORMULA :

(a)f

1

u

1

v

1=

(b)f1 = ( 1)

21 R1

R1

(c) m =u

v


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EXERCISE # I

Q.1 A plane mirror 50 cm long , is hung parallel to a vertical wall of a room, with its lower edge 50 cm above

the ground. A man stands infront of the mirror at a distance 2 m away from the mirror. If his eyes are at

a height 1.8 m above the ground, find the length of the floor between him & the mirror, visible to him

reflected from the mirror.

Q.2 In figure shown AB is a plane mirror of length 40cm placed at a height 40cmfrom ground. There is a light source S at a point on the ground. Find the minimum

and maximum height of a man (eye height) required to see theimage of the source if he is standing at a point A on ground shown in figure.

Q.3 A plane mirror of circular shape with radius r = 20 cm is fixed to the ceiling. A bulb is to be placed on the

axis of the mirror. A circular area of radius R = 1 m on the floor is to be illuminated after reflection of light

from the mirror. The height of the room is 3m. What is maximum distance from the center of the mirror

and the bulb so that the required area is illuminated?

Q.4 A light ray I is incident on a plane mirror M. The mirror is rotated in the

direction as shown in the figure by an arrow at frequency9 rev/sec.

The light reflected by the mirror is received on the wall W at a distance

10 m from the axis of rotation. When the angle of incidence becomes

37 find the speed of the spot (a point) on the wall?

Q.5 A concave mirror of focal length 20 cm is cut into two parts from the

middle and the two parts are moved perpendicularly by a distance 1 cm

from the previous principal axis AB. Find the distance between the

images formed by the two parts?

Q.6 A balloon is rising up along the axis of a concave mirror of radius of curvature 20 m. A ball is dropped

from the balloon at a height 15 m from the mirror when the balloon has velocity 20 m/s. Find the speed

of the image of the ball formed by concave mirror after 4 seconds? [Take : g=10 m/s2]

Q.7 A thin rod of length d/3 is placed along the principal axis of a concave mirror of focal length = d such that

its image, which is real and elongated, just touches the rod. Find the length of the image?

Q.8 A point object is placed 33 cm from a convex mirror of curvature radius = 40 cm. A glass plate of

thickness 6 cm and index 2.0 is placed between the object and mirror, close to the mirror. Find the

distance of final image from the object?

Q.9 A long solid cylindrical glass rod of refractive index 3/2 is immersed in a

liquid of refractive index4

33 . The ends of the rod are perpendicular

to the central axis of the rod. a light enters one end of the rod at the

central axis as shown in the figure. Find the maximum value of angle for which internal reflection occurs inside the rod?


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Q.10 A slab of glass of thickness 6 cm and index 1.5 is place somewhere in between a concave mirror and apoint object, perpendicular to the mirror's optical axis. The radius of curvature of the mirror is 40 cm. If

the reflected final image coincides with the object, then find the distance of the object from the mirror?

Q.11 A ray of light enters a diamond (n = 2) from air and is being internally

reflected near the bottom as shown in the figure. Find maximum value of

angle possible?

Q.12 A ray of light falls on a transparent sphere with centre at C as shown in

figure. The ray emerges from the sphere parallel to line AB. Find the

refractive index of the sphere.

Q.13 A beam of parallel rays of width b propagates in glass at an angle to itsplane face . The beam width after it goes over to air through this face is

_______ if the refractive index of glass is.

Q.14 A cubical tank (of edge l) and position of an observer are shown in the figure.

When the tank is empty, edge of the bottom surface of the tank is just visible. An

insect is at the centre C of its bottom surface. To what height a transparent liquid

of refractive index =2

5must be poured in the tank so that the insect will

become visible?

Q.15 Light from a luminous point on the lower face of a 2 cm thick glass slab, strikes the upper face and the

totally reflected rays outline a circle of radius 3.2 cm on the lower face. What is the refractive index of theglass.

Q.16 A ray is incident on a glass sphere as shown. The opposite surface of the

sphere is part ially silvered. If the net deviation of the ray transmitted at the

partially silvered surface is 1/3 rd of the net deviation suffered by the ray

reflected at the partially silvered surface (after emerging out of

the sphere). Find the refractive index of the sphere.

Q.17 A narrow parallel beam of light is incident on a transparent sphere of refractive index 'n'. If the beam finally

gets focussed at a point situated at a distance = 2 (radius of sphere) from the centre of the sphere, then

find n?

Q.18 A uniform, horizontal beam of light is incident upon a quarter cylinder of

radius R = 5 cm, and has a refractive index 32 . A patch on the table for

a distance 'x' from the cylinder is unilluminated. find the value of 'x'?


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Q.19 A point object is placed at a distance of 25 cm from a convex lens of focal length 20 cm. If a glass slabof thickness t and refractive index 1.5 is inserted between the lens and object. The image is formed at

infinity. Find the thickness t ?

Q.20 An object is kept at a distance of 16 cm from a thin lens and the image formed is real. If the object is kept

at a distance of 6 cm from the same lens the image formed is virtual. If the size of the image formed are

equal, then find the focal length of the lens?

Q.21 A thin convex lens forms a real image of a certain object p times its size. The size of real image becomesq times that of object when the lens is moved nearer to the object by a distance a find focal length of

the lens ?

Q.22 In the figure shown, the focal length of the two thin convex lenses is

the same = f. They are separated by a horizontal distance 3f and

their optical axes are displaced by a vertical separation 'd' (d


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EXERCISE # II

Q.1 An observer whose least distance of distinct vision is 'd', views his own face in a convex mirror of radius

of curvature 'r'. Prove that magnification produced can not exceed22 rdd

r

++.

Q.2 A thief is running away in a car with velocity of 20 m/s. A police jeep is following him, which is sighted bythief in his rear view mirror which is a convex mirror of focal length 10 m. He observes that the image of

jeep is moving towards him with a velocity of 1 cm/s. If the magnification of the mirror for the jeep at thattime is 1/10. Find

(a) actual speed of jeep(b) rate at which magnification is changing.

Assume that police jeep is on axis of the mirror.

Q.3 A luminous point P is inside a circle. A ray enters from P and after two reflections by the circle, return to P.I fI fI fI f be the angle of incidence, a the distance of P from the centre of the circle and b the distance of the

centre from the point where the ray in its course crosses the diameter through P, prove that tan=ba

ba

+

.

Q.4 An object is kept on the principal axis of a convex mirror of focal length 10 cm at a distance of 10 cm

from the pole. The object starts moving at a velocity 20 mm/sec towards the mirror at angle 30 with theprincipal axis. What will be the speed of its image and direction with the principal axis at that instant?

Q.5 A surveyor on one bank of canal observed the image of the 4 inch and 17 ft marks on a vertical staff,

which is partially immersed in the water and held against the bank directly opposite to him, coincides. Ifthe 17ft mark and the surveyors eye are both 6ft above the water level, estimate the width of the canal,

assuming that the refractive index of the water is 4/3.

Q.6 A circular disc of diameter d lies horizontally inside a metallic hemisphericalbowl radius a. The disc is just visible to an eye looking over the edge. Thebowl is now filled with a liquid of refractive index . Now, the whole of the

disc is just visible to the eye in the same position. Show that d = 2a )1(

)1(2

2

+

.

Q.7 A ray of light travell ing in air is incident at grazing angle

(incidence angle = 90) on a medium whose refractive index depends

on the depth of the medium. The trajectory of the light in the medium isa parabola, y = 2x2. Find, at a depth of 1 m in the medium.

(i) the refractive index of the medium and(ii) angle of incidence .

Q.8 Two thin similar watch glass pieces are joined together, front to front, with rear portion silvered and the

combination of glass pieces is placed at a distance a = 60 cm from a screen. A small object is placednormal to the optical axis of the combination such that its two times magnified image is formed on the

screen. If air between the glass pieces is replaced by water ( = 4/3), calculate the distance throughwhich the object must be displaced so that a sharp image is again formed on the screen.

Q.9 A concave mirror has the form of a hemisphere with a radius of R = 60 cm. A thin layer of an unknowntransparent liquid is poured into the mirror. The mirror-liquid system forms one real image and another

real image is formed by mirror alone, with the source in a certain position. One of them coincides with

the source and the other is at a distance ofl = 30 cm from source. Find the possible value(s) refractive

index of the liquid.


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Q.10 In the figure shown, find the relative speed of approach/separation of thetwo final images formed after the light rays pass through the lens, at the

moment when u = 30 cm. The speed object = 4 cm/s. The two lens halvesare placed symmetrically w.r.t. the moving object.

Q.11 In the figure shown L is a converging lens of focal length 10cm

and M is a concave mirror of radius of curvature 20cm. A pointobject O is placed in front of the lens at a distance 15cm. AB and

CD are optical axes of the lens and mirror respectively. Find thedistance of the final image formed by this system from the optical

centre of the lens. The distance between CD & AB is 1 cm.

Q.12 A thin plano-convex lens fits exactly into a plano concave lens with their plane

surface parallel to each other as shown in the figure. The radius of curvature of

the curved surface R = 30 cm. The lens are made of difference

m a t e r i a l h a v i n g r e f r a c t i v e i n d e x m a t e r i a l h a v i n g r e f r a c t i v e i n d e x m a t e r i a l h a v i n g r e f r a c t i v e i n d e x m a t e r i a l h a v i n g r e f r a c t i v e i n d e x 1 = 2

3and 2 = 4

5as shown in figure.

(i) if plane surface of the plano-convex lens is silvered, then calculate the equivalent

focal length of this system and also calculate the nature of this equivalent mirror.

(ii) An object having transverse length 5 cm in placed on the axis of equivalent mirror (in part 1), at adistance 15 cm from the equivalent mirror along principal axis. Find the transverse magnification produced

by equivalent mirror.

Q.13 In the figure shown O is point object. AB is principal axis of the converging

lens of focal length F. Find the distance of the final image from the lens.

Q.14 The rectangular box shown is the place of lens. By

looking at the ray diagram, answer the following

questions:(i) If X is 5 cm then what is the focal length of the lens?(ii) If the point O is 1 cm above the axis then what is the

position of the image? Consider the opt ical center of

the lens to be the origin.

Q.15 Two identical convex lenses L1 and L2 are placed at a distance of 20 cm from each other on the common

principal axis. The focal length of each lens is 15 cm and the lens L2 is to the right o f lens A. A point

object is placed at a distance of 20 cm on the left of lens L1, on the common axis of two lenses. Find,

where a convex mirror of radius of curvature 5 cm should be placed so that the final image coincides with

the object?

Q.16 An isosceles triangular glass prism stands with its base in water as shown. The

angles that its two equal sides make with the base are each. An incident ray oflight parallel to the water surface internally reflects at the glass-water interface

and subsequently re-emerges into the air. Taking the refractive indices of glass

and water to be 3/2 and 4/3 respectively, show that must be at least

tan117

2or 25.9.


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Q.17 A parallel beam of light falls normally on the first face of a prism of small angle. At the second face it ispartly transmitted and partly reflected, the reflected beam striking at the first face again, and emergingfrom it in a direction making an angle 630' with the reversed direction of the incident beam. The refractedbeam is found to have undergone a deviation of 115' from the o riginal direction. Find the refractiveindex of the glass and the angle of the prism.

Q.18 The refractive indices of the crown glass for violet and red lights are

1.51 and 1.49 respectively and those of the flint glass are 1.77 and 1.73respectively. A prism of angle 6 is made o f crown glass. A beam ofwhite light is incident at a small angle on this prism. The other thin flintglass prism is combined with the crown glass prism such that the netmean deviation is 1.5 anticlockwise.

(i) Determine the angle of the flint glass prism.(ii) A screen is placed normal to the emerging beam at a distance of 2m from the prism combination. Find

the distance between red and violet spot on the screen. Which is the topmost colour on screen.


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EXERCISE # III

Q.1 A ray of light travelling in air is incident at grazing angle (incidentangle = 90) on a long rectangular slab of a transparent mediumof thickness t = 1.0 (see figure). The point of incidence is theorigin A (O, O). The medium has a variable index of refractionn(y) given by : n(y) = [ky3/2 + 1]1/2, where k = 1.0 m3/2 .The refractive index of air is 1.0 .

(i) Obtain a relation between the slope of the trajectory of the ray at a point B(x,y) in the medium and theincident angle at that point.

(ii) Obtain an equation for the trajectory y(x) of the ray in the medium.(iii) Determine the coordinates (x

1, y

1) of the point P, where the ray the ray intersects the upper surface of

the slab-air boundary .(iv) Indicate the path of the ray subsequently . [JEE 95]

Q.2 A right angle prism (459045) of refractive index n has a plateof refractive index n

1(n

1< n) cemented to its diagonal face. The assembly

is in air. a ray is incident on AB (see the figure) .(i) Calculate the angle of incidence at AB for which the ray strikes the

diagonal face at the critical angle.(ii) Assuming n = 1.352 . Calculate the angle of incidence at AB for which the refracted ray passes through

the diagonal face undeviated . [JEE 96]

Q.3 A thin planoconvex. Lens of focal length F is split into two halves,one of the halves is shifted along the optical axis. The separation betweenobject and image planes is 1.8 m. The magnification of the image formedby one of the half lenses is 2. Find the focal length of the lens andseparation between the two halves. Draw the ray diagram for imageformation. [JEE 96]

Q.4 Which of the following form(s) a virtual & erect image for all positions of the real object ?(A) Convex lens (B) Concave lens (C) Convex mirror (D) Concave mirror

[JEE 96]

Q.5 A small fish, 0.4 m below the surface of a lake, is viewed through a simple converging lens of focallength 3m . The lens is kept at 0.2m above the water surface such that the fish lies on the optical axis ofthe lens. Find the image of the fish seen by the observer . The refractive index of the water is 4/3.

[REE 96]

Q.6(i)An eye specialist prescribes spectacles having a combination of convex lens of focal length 40cm incontact with a concave lens of focal length 25 cm . The power of this lens combination in diopters is :

(A) + 1.5 (B) 1.5 (C) + 6.67 (D)

6.67 [JEE '97]


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(ii) A thin equiconvex lens of glass of refractive index =3/2& of focal length 0.3 m in air is sealed into an openingat one end of a tank filled with water ( = 4/3). On theopposite side of the lens, a mirror is placed inside thetank on the tank wall perpendicular to the lens axis, asshown in figure . The separation between the lens and themirror is 0.8 m . A small object is placed outside the tank

in front of the lens at a distance of 0.9 m from the lensalong its axis . Find the position (relative to the lens) of theimage of the object formed by the system. [JEE ' 97]

Q.7 Select the correct alternative(s) : [JEE '98](i) A concave mirror is placed on a horizontal table, with its axis directed vertically upwards. Let O be

the pole of the mirror & C its centre of curvature . A point object is placed at C . It has a real image, alsolocated at C . If the mirror is now filled with water, the image will be:(A) real, & will remain at C(B) real, & located at a point between C &(C) virtual, & located at a point between C & O(D) real, & located at a point between C & O .

(ii) A ray of light travelling in a transparent medium falls on a surface separating the medium from air at anangle of incidence of 45 . The ray undergoes total internal reflection . If n is the refractive index of themedium with respect to air, select the possible value(s) of n from the following :(A) 1.3 (B) 1.4 (C) 1.5 (D) 1.6

(iii) A spherical surface of radius of curvature R separates air (refractive index 1.0) from glass (refractiveindex 1.5) . The centre of curvature is in the glass . A point object P placed in air is found to have areal image Q in the glass . The line PQ cuts the surface at a point O and PO = OQ . The distance POis equal to :(A) 5R (B) 3R (C) 2R (D) 1.5R

Q.8 A prism of refractive index n1

& another prism of refractive index n2

are stuck together without a gap as shown in the figure. The anglesof the prisms are as shown . n

1& n

2depend on , the wavelength of

light according to n1= 1.20 + 2

4108.10

& n

2= 1.45 + 2

41080.1

where is in nm .(i) Calculate the wavelength

0for which rays incident at any angle on the interface BC pass through

without bending at that interface .(ii) For light of wavelength

0, find the angle of incidence i on the face AC such that the deviation produced

by the combination of prisms is minimum . [JEE '98]

Q.9 A rod made of glass ( = 1.5) and of square cross-section is bent into the shapeshown in figure. A parallel beam of light falls perpendicularly on the plane flat surfaceA. Referring to the diagram, d is the width of a side & R is the radius of inner

semicircle. Find the maximum value of ratioR

dso that all light entering the glass

through surface A emerge from the glass through surface B. [REE '98]


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Q.10 A concave lens of glass, refractive index 1.5, has both surfaces of same radius of curvature R. Onimmersion in a medium of refractive index 1.75, it will behave as a [JEE 99](A) convergent lens of focal length 3.5R (B) convergent lens of focal length 3.0 R.(C) divergent lens of focal length 3.5 R (D) divergent lens of focal length 3.0 R

Q.11 The x-y plane is the boundary between two transparent media. Medium-1 with z > 0 has refractive index

2 and medium 2 with z < 0 has a refractive index 3 . A ray of light in medium 1 given by the

vector k10j38i36A += is incident on the plane of separation. Find the unit vector in the

direction of refracted ray in medium -2. [JEE 99]

Q.12 A quarter cylinder of radius R and refractive index 1.5 is placed on a table. A pointobject P is kept at a distance of mR from it. Find the value of m for which a ray fromP will emerge parallel to the table as shown in the figure. [JEE '99]

Q.13 Two symmetric double-convex lenses L1and L

2with their radii of curvature 0.2m each are made from

glasses with refractive index 1.2 and 1.6 respectively. The lenses with a separation of 0.345 m aresubmerged in a transparent liquid medium with a refractive index of 1.4. Find the focal lengths of lens L

1

and L2

. An object is placed at a distance of 1.3m from L1

, find the location of its image while the wholesystem remains inside the liquid. [REE 99]

Q.14 Select the correct alternative. [JEE '2000 (Scr)](a) A diverging beam of light from a point source S having divergence angle, falls

symmetrically on a glass slab as shown. The angles of incidence of the twoextreme rays are equal. If the thickness of the glass slab is t and the refractiveindex n, then the divergence angle of the emergent beam is(A) zero (B) (C) sin1(1/n) (D) 2sin1(1/n)

(b) A rectangular glass slab ABCD, of refractive index n1, is immersed in water

of refractive index n2(n1> n2). A ray of light is incident at the surface AB of theslab as shown. The maximum value of the angle of incidence

max, such that

the ray comes out only from the other surface CD is given by

(A)

1

21

2

11

n

nsincos

n

nsin (B)

2

11

1

n

1sincosnsin

(C)

2

11

n

nsin (D)

1

21

n

nsin

(c) A point source of light B is placed at a distance L in front of the centre of a

mirror of width d hung vertically on a wall. A man walks in front of the mirroralong a line parallel to the mirror at a distance 2L from it as shown. The greatestdistance over which he can see the image of the light source in the mirror is(A) d/2 (B) d (C) 2d (D) 3d


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(d) A hollow double concave lens is made of very thin transparent material. It can be filled with air or eitherof two liquids L

1or L

2having refractive indices n

1and n

2respectively (n

2> n

1> 1). The lens will diverge

a parallel beam of light if it is filled with(A) air and placed in air. (B) air and immersed in L

1.

(C) L1

and immersed in L2. (D) L

2and immersed in L

1.

Q.15 A convex lens of focal length 15 cm and a concave mirror of focal length

30 cm are kept with their optic axes PQ and RS parallel but separatedin vertical direction by 0.6 cm as shown. The distance between the lensand mirror is 30 cm. An upright object AB of height 1.2 cm is placed onthe optic axis PQ of the lens at a distance of 20 cm from the lens . If AB is the image after refraction from the lens and reflection from themirror, find the distance AB from the pole of the mirror and obtain itsmagnification. Also locate positions of A and Bwith respect to theoptic axis RS. [JEE 2000]

Q.16 A thin equi biconvex lens of refractive index 3/2 is placed on a horizontalplane mirror as shown in the figure. The space between the lens and themirror is then filled with water of refractive index 4/3. It is found that

when a point object is placed 15cm above the lens on its principalaxis, the object coincides with its own image. On repeating with anotherliquid, the object and the image again coincide at a distance 25cm fromthe lens. Calculate the refractive index of the liquid. [JEE 2001]

Q.17 The refractive indices of the crown glass for blue and red lights are 1.51 and 1.49 respectively and thoseof the flint glass are 1.77 and 1.73 respectively. An isosceles prism of angle 6 is made of crown glass.A beam of white light is incident at a small angle on this prism. The other flint glass isosceles prism iscombined with the crown glass prism such that there is no deviation of the incident light. Determine theangle of the flint glass prism. Calculate the net dispersion of the combined system. [JEE 2001]

Q.18 An observer can see through a pin-hole the top end of a thin rod ofheight h, placed as shown in the figure. The beaker height is 3h and itsradius h. When the beaker is filled with a liquid up to a height 2h, he cansee the lower end of the rod. Then the refractive index of the liquid is

(A) 5/2 (B) 2/5

(C) 2/3 (D) 3/2 [JEE 2002 (Scr)]

Q.19 Which one of the following spherical lenses does not exhibit dispersion? The radii of curvature of thesurfaces of the lenses are as given in the diagrams. [JEE 2002 (Scr)]

(A) (B) (C) (D)


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Q.20 Two plane mirrors A and B are aligned parallel to each other, as shownin the figure. A light ray is incident at an angle of 30 at a point just insideone end o f A. The plane of incidence coincides with the plane of thefigure. The maximum number of times the ray undergoes reflections(including the first one) before it emerges out is [JEE 2002 (Scr)](A) 28 (B) 30 (C) 32 (D) 34

Q.21 A convex lens of focal length 30 cm forms an image of height 2 cm for an object situated at infinity. If aconvcave lens of focal length 20 cm is placed coaxially at a distance of 26 cm in front of convex lens thensize image would be [JEE 2003 (Scr)](A) 2.5 cm (B) 5.0 (C) 1.25 (D) None

Q.22 A meniscus lens is made of a material of refractive index2. Both its surfaceshave radii of curvature R. It has two different media of refractive indices1and 3 respectively, on its two sides (see figure). Calculate its focal length for1 < 2 < 3, when light is incident on it as shown. [JEE 2003]

Q.23 White light is incident on the interface of glass and air as shown in the figure. If

green light is just totally internally reflected then the emerging ray in air contains(A) yellow, orange, red (B) violet, indigo, blue(C) all colours (D) all coloure except green

[JEE 2004 (Scr)]

Q.24 A ray of light is incident on an equilateral glass prism placed on a horizontaltable. For minimum deviation which of the following is true ? [JEE 2004 (Scr)](A) PQ is horizontal (B) QR is horizontal(C) RS is horizontal (D) Either PQ or RS is horizontal.

Q.25 A point object is placed at the centre of a glass sphere of radius 6 cm and refractive index 1.5. The

distance of the virtual image from the surface of the sphere is [JEE 2004 (Scr)](A) 2 cm (B) 4 cm (C) 6 cm (D) 12 cm

Q.26 Figure shows an irregular block of material of refractive index 2 . AA

ray of light strikes the face AB as shown in the figure. After refraction itis incident on a spherical surface CD of radius of curvature 0.4 m andenters a medium of refractive index 1.514 to meet PQ at E. Find thedistance OE upto two places of decimal. [JEE 2004]

Q.27 An object is approaching a thin convex lens of focal length 0.3 m with a speed of 0.01 m/s. Find themagnitudes of the rates of change of position and lateral magnification of image when the object is at a

distance of 0.4 m from the lens. [JEE 2004]

Q.28 The ratio of powers of a thin convex and thin concave lens is2

3and equivalent focal length of their

combination is 30 cm. Then their focal lengths respectively are [JEE' 2005 (Scr)](A) 75, 50 (B) 75, 50 (C) 10, 15 (D) 75, 50


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Page17of20GEOMETRICALOPTICSQ.29 Figure shows object O. Final image Iis formed after two refractions and one

reflection is also shown in figure. Find the focal length of mirror. (in cm) :(A) 10 (B) 15 (C) 20 (D) 25

[JEE' 2005 (Scr)]

Q.30 What will be the minimum angle of incidence such that the total internal reflectionoccurs on both the surfaces?[JEE 2005]

Q.31 Two identical prisms of refractive index 3 are kept as shown in the figure. A light ray strikes the first

prism at face AB. Find,(a) the angle of incidence, so that the emergent ray from the first prism has

minimum deviation.(b) through what angle the prism DCE should be rotated about C so that

the final emergent ray also has minimum deviation.[JEE 2005]

Q.32 A point object is placed at a distance of 20 cm from a thin plano-convex lens of focallength 15 cm, if the plane surface is silvered. The image will form at(A) 60 cm left of AB(B) 30 cm left of AB(C) 12 cm left of AB(D) 60 cm right of AB [JEE 2006]

Q.33 Graph of position of image vs position of point object from a convexlens is shown. Then, focal length of the lens is(A) 0.50 0.05 cm(B) 0.50 0.10 cm

(C) 5.00 0.05 cm(D) 5.00 0.10 cm [JEE 2006]

Q.34 Parallel rays of light from Sun falls on a biconvex lens of focal length f and the circular image of radius ris formed on the focal plane of the lens. Then which of the following statement is correct?(A)Area of image r2 directly proportional to f(B) Area of image r2 directly proportional to f2

(C) Intensity of image increases if f is increased.(D) If lower half of the lens is covered with black paper area of image will become half. [JEE 2006]

Q.35 A simple telescope used to view distant objects has eyepiece and objective lens of focal lengths fe and f0,respectively. Then [JEE 2006]

Column 1 Column 2

(A) Intensity of light received by lens (P) Radius of aperture (R)(B) Angular magnification (Q) Dispersion of lens(C) Length of telescope (R) focal length f 0, fe(D) Sharpness of image (S) spherical aberration


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ANSWER KEY

EXERCISE # I

Q.1 1.23 m Q.2 160cm; 320cm Q.3 75 cm Q.4 1000 m/sQ.5 2 cm Q.6 80 m/s Q.7 d/2 Q.8 42 cm

Q.9

31sin 1 Q.10 42 cm Q.11 sin1

2

13 Q.12 3

Q.13

sin

)cos1(b 2/122Q.14 h = l Q.15

4

41Q.16 3

Q.17 4/3 Q.18 5 cm Q.19 15 cm Q.20 11 cm

Q.21)pq(

apq

Q.22 (5f, 2d) Q.23 (/4) cm2 Q.24 3 cm

Q.25 75/4 cm, 75/2 cm Q.26 (i) 0.2 m ,(ii) 0.4 m Q.27 1.5

Q.28 45 Q.29 5

43

Q.30 25

8

EXERCISE # II

Q.2 (a) 21 m/s, (b) 1 103 /sec Q.4 tan13

2with the principal axis,

4

7cm/sec

Q.5 16 feet Q.7 = 3, sin1(1/3) Q.8 15 cm towards the combination

Q.9 1.5 or )15( Q.10 8/5 cm/s Q.11 266 cm Q.12 + 60, + 4/5

Q.13 l = 22fd2fd4

fd)d2f3(

Q.14 10cm, 10,2 Q.15 5.9 cm,10.9 cm

Q.17 =8

13, A = 2 Q.18 (i) 2 ,(ii) mm

9

4

EXERCISE # III

Q.1 (a) tan =d y

d x= cot i (b) y = k2

x

4

4

(c) 4.0, 1 (d) It will become parallel to x-axis

Q.2 (i) sin11

2

21

21n n n

(ii) r

1= sin1 (n sin 45) = 72.94

Q.3 f = 0.4 m, separation = 0.6m Q.4 B,C Q.5 On the object itself

Q.6 (i) B, (ii) 90 cm from the lens towards right Q.7 (i) D, (ii) C, D, (iii) A

Q.8 (i) 0

= 600 nm, n = 1.5 (ii) i = sin1 (0.75) = 48.59 Q.9r

R

max

=1

2Q.10 AA

Q.11 )45r;60incidenceofangle(k2

1j

5

22i

25

3r 00 ==+=

Q.12 m = 4/3


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Q.13 f1

= -70cm, f2

= 70cm, V= 560 cm to the right of L2

Q.14 (a) B (b) A (c) D (d) D

Q.15 AB at 15 cm to the right of mirror . B is 0.3 cm above RS and A is 1.5 cm below RS. Magnificationis 1.5

Q.16 1.6 Q.17 40 and 0.040 Q.18 B Q.19 C Q.20 B

Q.21 A Q.2213

3Rvf

== Q.23 A Q.24 B

Q.25 C Q.26 06.61.0

4.0514.1=

m correct upto two places of decimal.

Q.27 0.09 m/s ; Magnitude of the rate of change of lateral magnification is 0.3 s1. Q.28 C

Q.29 C Q.30 60 Q.31 (a) i = 60, (b) 60 (anticlockwise)

Q.32 C Q.33 C Q.34 B

Q.35 (A) P ; (B) R; (C) R; (D) P, Q, S

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Geometrical Optics Problems